An Improved Method of the Finite-Difference Sparse Phase Unwrapping

Phase unwrapping (PU) is a significant problem for reconstructing the deformation field during synthetic aperture radar interferometry analysis. The various 2-D PU algorithms can be divided into two categories: path-following methods and optimization-based methods. The former predefine an integration path in which the phase gradient is integrated to obtain the unwrapped results. The latter are path independent and error criterion oriented. The integration of the finite differences and the minimum cost flow solver describes a global optimization problem between the phase residues over closed spatial triangles computed over redundant neighboring edge sets. We propose a modified network using a simplified mathematical formulation for linear programming (LP) in the finite differences PU. Our algorithm has three major advantages over current methods. First, the modified network combines the Delaunay triangulation and K nearest points to avoid isolated regions in the PU process. Second, modified formulation of the LP solver can directly obtain the phase ambiguity cycles of all points without integration. Finally, the combination of the new network and modified LP can achieve better PU results than the other state-of-the-art techniques. We applied our method to synthetic and real data from January 24, 2020 Mw 6.7 earthquake in Doğanyol-Sivrice, Turkey to August 8, 2017 Mw 6.5 earthquake in Jiuzhaigou, China. Comprehensive comparisons validate the effectiveness of our method.